A log-adjusted t-statistic for large clinical laboratory datasets: a simulation study and real-world application

In large datasets, conventional t-tests may identify statistically significant but practically trivial differences because statistical significance increases with sample size. A log-adjusted t-statistic, defined as an empirical sample-size-aware modification of the classical t-statistic, was evaluated to reduce this oversensitivity. Performance was assessed by Monte Carlo simulations of two-sample comparisons across sample sizes from 10 to 50,000 and effect sizes from δ = 0 to 1.0, and by application to a real clinical laboratory dataset comprising 464,145 participants. In simulations, the ${\text{log}}_{10}\left(\text{Df}\right)$-adjusted statistic showed null rejection rates close to 0.05 across sample sizes, whereas the classical t-test became increasingly oversized at very large n. The adjustment was more conservative for small effects (δ = 0.2-0.4) while high rejection rates were retained for larger effects (δ = 0.6-1.0). In the real-data analysis, several sex differences that were highly significant by the classical t-test had small effect sizes and yielded reference p-values above the conventional 0.05 threshold after adjustment; platelet count (Cohen's d = 0.13) changed from p < 10^-300 to reference p = 0.052, and potassium (d = 0.05) from p = 10-51 to reference p = 0.104. In contrast, larger effects such as hematocrit (d = 0.83) and HDL cholesterol (d = 0.77) continued to yield reference p-values below that threshold. These reference p-values were compared with the conventional α = 0.05 threshold for illustrative purposes only and were not intended to imply formal Type I error control. These findings suggest that the log-adjusted t-statistic may serve as a useful empirical decision aid for interpreting large clinical laboratory datasets by attenuating sample-size-driven significance while preserving detection of substantively meaningful effects.